$I n a △ A B C = ∠ C = 3 ∠ B = 2 (∠ A + ∠ B), t h e n ∠ B = ? (a) 20^{\circ} (b) 40^{\circ} (c) 60^{\circ} (d) 80^{\circ}$

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Solution

Let $∠ C = 3 ∠ B = 2 (∠ A + ∠ B) = x$
$∠ C$ =x, -----(1)
3 $∠ B$ =x
$∠ B$ =x/3----(2)
2 $∠ (A + B)$ =x
$∠ A + ∠ B$ =x/2
$∠ A$ =x/2 - $∠ B$
$∠ A$ =x/2-x/3-----(3)
sum of the three angles in a triangle is 180degree
$∠ A + ∠ B + ∠ C$ =180
x/2-x/3+x/3+x=180[from(1),(2),(3)]
(3x-2x+2x+6x)/6=180
9x/6=180
x=1806/9
x=206
x=120

therefore
A= x/2-x/3=120/2-120/3=60-40=20
B=x/3=120/3=40
C=x=120

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